Question

select the correct answer. which graph represents the solution to this inequality? $-\frac{1}{4}(12x + 8) \leq -2x + 11$ a. graph a b. graph b c. graph c d. graph d

Explanation:

Step1: Simplify the inequality

Start with the inequality \(-\frac{1}{4}(12x + 8) \leq -2x + 11\). First, distribute the \(-\frac{1}{4}\) on the left side:

$$ -\frac{1}{4} \times 12x - \frac{1}{4} \times 8 \leq -2x + 11 $$

Simplify each term: \(-3x - 2 \leq -2x + 11\).

Step2: Solve for \(x\)

Add \(3x\) to both sides to get: \(-2 \leq x + 11\). Then subtract \(11\) from both sides: \(-2 - 11 \leq x\), which simplifies to \(-13 \leq x\) (or \(x \geq -13\)).

Step3: Analyze the graphs

We need a number line with a closed circle at \(-13\) (since the inequality is "less than or equal to" or "greater than or equal to", so the point is included) and the arrow pointing to the right (since \(x\) is greater than or equal to \(-13\)). Looking at the options:

• Option A: Closed circle at \(-9\), arrow left – incorrect.
• Option B: Closed circle at \(-13\), arrow right – matches our solution.
• Option C: Closed circle at \(-13\), arrow left – incorrect.
• Option D: Closed circle at \(-9\), arrow right – incorrect.

Answer:

B. (The graph with a closed circle at -13 and an arrow pointing to the right)